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- Thread starter PreposterousUniverse
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I'm not sure what you mean bye "decompose the electromagnetic tensor F into the E and B under spatial rotations". Maybe the most simple answer is to use the representation for the full proper orthochronous Lorentz group in terms of ##\mathrm{SO}(3,\mathbb{C})##. This is how the Riemann-Silberstein vector ##\vec{F}=\mathrm{E}+\mathrm{i} \vec{B}## transforms under proper orthochronous Lorentz transformations. The usual rotations are of course represented by the subgroup SO(3) of ##\mathrm{SO}(3,\mathbb{C})##. This means of course that ##\vec{E}## and ##\vec{B}## transform within each other by rotations. A pure rotation-free boost along a given direction is represented by the usual rotation matrix but with an purely imaginary angle, i.e., a boost always mixes electric and magnetic field components.

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